{
  "id": 1143,
  "curve_key": "854607185671736492193512161:24935617390364032840850084799609528755759",
  "ainvs": [
    "1",
    "0",
    "0",
    "-17804316368161176920698170",
    "-28860668275885780962533093060587753500"
  ],
  "rank_lower_bound": 5,
  "torsion": [
    2,
    2
  ],
  "naive_height": 186.03805248977932,
  "faltings_height": 13.300769392932056,
  "conductor": "138952056675401970",
  "bad_primes": [
    "2",
    "3",
    "5",
    "7",
    "11",
    "13",
    "19",
    "47",
    "59",
    "73",
    "347",
    "3467"
  ],
  "discriminant": "1377479632666872463261645551040351718160097205332763153831191715029472774400",
  "regulator": "650507.429405225019947489897014689568671923173672",
  "points": [
    [
      "-16604870452958076300/6754801",
      "-3988277467568331091290844950/17555727799"
    ],
    [
      "-3955975540920654510/1615441",
      "477153039011132864705198790/2053225511"
    ],
    [
      "-2350103741370",
      "41575475331057360"
    ],
    [
      "-11660356860822915/4624",
      "-10212576192621072614295/314432"
    ],
    [
      "-13952033926182072610974/5535508801",
      "21099728055008301932226264596682/411847390303201"
    ]
  ],
  "submitter": "David Renshaw",
  "history": [],
  "commentary": "Obtained by computing a rational isogeny from curve#1088 and mapping all 5 independent witness points to the global minimal model. Isogenies preserve the Mordell-Weil rank; the image points are independently certified by the site verifier. Torsion computed exactly with PARI/GP elltors. Conductor is unchanged by the isogeny.",
  "created_at": "2026-09-23 21:37:27",
  "updated_at": "2026-09-23 21:37:27"
}